integral of sin^2u

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(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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integral sin²(u)

Solution

12 (u−12 sin(2u))+C

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∫ sin²(u)du

Rewrite using trig identities

=∫ 1−cos(2u)2 du

Take the constant out: ∫a·f(x)dx=a·∫f(x)dx

=12 · ∫ 1−cos(2u)du

Apply the Sum Rule: ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx

=12 (∫ 1du−∫ cos(2u)du)

∫ 1du=u

∫ cos(2u)du=12 sin(2u)

=12 (u−12 sin(2u))

Add a constant to the solution

=12 (u−12 sin(2u))+C

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

integral of sin^2u

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